and many more benefits!

Find us on Facebook

GMAT Club Timer Informer

Hi GMATClubber!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Hide Tags

Show Tags

21 Jan 2012, 04:07

1

This post receivedKUDOS

5

This post wasBOOKMARKED

00:00

A

B

C

D

E

Difficulty:

85% (hard)

Question Stats:

54%(02:00) correct 46%(01:41) wrong based on 162 sessions

HideShow timer Statistics

If the volume of the cone is SH/3 where S is the area of the base and H the height. AB=BC. What is the ratio of the volume of the cone (with BC as height) to the volume of the rest of the cone (with AB as height). (for graph see attached. Didn't know how to add picture to this post)

1. 1:32. 1:43. 1:64. 1:75. 1:8

Thanks for helping. I must have forgotten something about cone characteristics here...

Show Tags

If the volume of the cone is SH/3 where S is the area of the base and H the height. AB=BC. What is the ratio of the volume of the cone (with BC as height) to the volume of the rest of the cone (with AB as height). (for graph see attached. Didn't know how to add picture to this post)

1. 1:32. 1:43. 1:64. 1:75. 1:8

Thanks for helping. I must have forgotten something about cone characteristics here...

Note that the wording is not 100% accurate, plus it's highly unlikely you'll need this staff for the GMAT.

Attachment:

untitled.JPG [ 13.91 KiB | Viewed 4504 times ]

Anyway, notice that since AB=BC (AC=2*BC) then R=2r (from similar triangles property). Now, the area of the base of a little upper cone (cone BC) will be \(s=\pi*r^2\) and as the area of the base of the bigger cone (cone AC) is \(S=\pi*R^2=\pi*4r^2=4s\) then \(s=\frac{S}{4}\).

Re: If the volume of the cone is SH/3 where S is the area of [#permalink]

Show Tags

29 May 2013, 01:25

1

This post receivedKUDOS

1

This post wasBOOKMARKED

I think the easiest way to solve this problem is keeping in mind the idea that if any dimension (for example, height h) of similar figures are in ratio 1:x, then their areas (S) will be in ratio 1:x^2, and their volumes will be in ratio 1:x^3

First,H(bc) - the height BCH(whole cone) - the height of the whole coneV(bc) - the volume of the smaller cone with the height BCV(ab) - the volume of the larger cone with the height ABV(whole cone) - the volume of the whole cone with the height AC

H(bc):H(whole cone) = 1:2, therefore V(bc):V(whole cone) = 1:8.

Let's V(bc) = x, then V(bc):V(whole cone) = x:8x.

Consequently, subtracting V(bc) from V(whole cone) we can calculate V(ab):V(ab) = 8x-x=7xand the ratio of the volume of the top half of the cone (with BC as height) to the volume of the bottom half of the cone (with AB as height) = x:7x = 1/7

Answer D

Last edited by thewind on 29 May 2013, 01:46, edited 2 times in total.

Re: If the volume of the cone is SH/3 where S is the area of [#permalink]

Show Tags

21 Aug 2017, 01:30

Splendidgirl666 wrote:

If the volume of the cone is SH/3 where S is the area of the base and H the height. AB=BC. What is the ratio of the volume of the cone (with BC as height) to the volume of the rest of the cone (with AB as height). (for graph see attached. Didn't know how to add picture to this post)

1. 1:32. 1:43. 1:64. 1:75. 1:8

Thanks for helping. I must have forgotten something about cone characteristics here...

Re: If the volume of the cone is SH/3 where S is the area of [#permalink]

Show Tags

25 Jan 2018, 11:57

One General concept, if two triangles are similar, and sides of the two triangles are in ratio = k : 1 then the area of the two triangles are in the ratio = k^2 : 1extending this concept to 3-D dimension, if two cones are similar(height1/height2 = radius1/radius), then the volume of the two cones are in the ratio = k^3 : 1